No, you have to use both slots at the same time :(
If you have an epic flying mount, you might want to consider repping up with the Netherwing flight. When you reach Honored or Revered, you get a trinket that gives +45 stam and the ability to summon a temporary pet :)
IRRC, there's also a PVP trinket that's a bit pricy on honor but also gives + 40/50 something stam